Known in the art are bottom-hole screw motors for drilling wells, working members of which form a multistart helical planetary gear mechanism. The mechanism includes a stator and a rotor. The stator comprises a casing internally provided with a resilient lining having the working surface in the form of a helical thread. The stator accommodates a rotor which is arranged eccentrically with respect to the stator and is externally provided with a helical thread.
The rotor and stator form a kinematic couple which is in permanent engagement similarly to an internal gearing, and they define closed cavities.
The axis of the rotor is displaced with respect to the axis of the stator by the amount of an eccentricity "e". the number of teeth of the helical surfaces of the stator and rotor correspond to the number of starts of their helical threads.
In the helical planetary gear mechanism the number of stator teeth is greater than the number of rotor teeth by unity. The ratio of stator and rotor pitches is directly proportional to the ratio of their teeth numbers.
Cycloidal gearing constitutes the basis for the formation of the cross-sectional configuration of a multistart helical planetary gear mechanism.
The cross-sectional shape of the stator is formed by alternating portions of cycloidal curves and arcs of circle. The cross-sectional shape of the rotor is formed by an envelope of the stator profile obtained by rolling maximum pitch circle of the rotor, chosen so as to ensure continuous engagement of the helical surfaces of the rotor and stator, inside an initial pre-set circle of the stator.
Geometrical parameters of working members of multistart screw motors are partially covered by U.S. Pat. No. 3,822,972 of Nov. 20, 1972, IPC F Olc 1/10, which teaches optimum dimensional proportioning of working members in the cross-section.
In screw motors, the three-dimensional configuration of helical surfaces of the rotor and stator depends on a parameter which represents the ratio of pitches of the helical surfaces of the stator and rotor to their respective pitch diameters. In prior art bottom-hole screw motors this parameter ranges from 4 to 4.6. Motors featuring a value of the parameter within this range are characterized by unstable starting performance resulting from the possibility of self-braking of working members of a motor.